The product of two co-prime numbers is 945 then find their LCM ?

Options

A. 189
B. 35
C. 27
D. 945

Answer

To find the Least Common Multiple (LCM) of two co-prime numbers whose product is given as 945, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Co-prime Numbers**:
Co-prime numbers are two numbers that have no common factors other than 1. This means that their highest common factor (HCF) is 1.

2. **Given Information**:
We are given that the product of two co-prime numbers \( N_1 \) and \( N_2 \) is 945.
\[ N_1 \times N_2 = 945 \]

3. **Using the Relationship Between LCM and HCF**:
The relationship between the LCM and HCF of two numbers is given by:
\[ \text{LCM}(N_1, N_2) \times \text{HCF}(N_1, N_2) = N_1 \times N_2 \]

4. **Substituting the Known Values**:
Since \( N_1 \) and \( N_2 \) are co-prime, we know that:
\[ \text{HCF}(N_1, N_2) = 1 \]
Therefore, substituting this into the relationship gives us:
\[ \text{LCM}(N_1, N_2) \times 1 = 945 \]

5. **Finding the LCM**:
This simplifies to:
\[ \text{LCM}(N_1, N_2) = 945 \]

6. **Conclusion**:
Thus, the LCM of the two co-prime numbers is:
\[ \text{LCM}(N_1, N_2) = 945 \]

### Final Answer:
The LCM of the two co-prime numbers is **945**.